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We present several improvements to three classical inequalities in analysis: Jensen's inequality, Hölder's inequality, and Hadamard's inequality. First, we establish new monotonicity results for Jensen's functional in the context of finite measures, extending known discrete cases. Besides, we provide a sharpened version of Hölder's inequality in measure spaces with atoms. Also, we analyse Hadamard's inequality for measures, proving its optimality.
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Quintana et al. (2026) studied this question.
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